Invertible elements of alternative unital ring form Moufang loop
Suppose is an alternative unital ring with multiplication . Suppose is the subset of comprising those elements of that possess two-sided inverses for . Then, is closed under and acquires the structure of a Moufang loop (?) under .
- Artin's theorem on alternative rings which states that for a ring, being alternative is the same as being diassociative.
- Alternative ring satisfies Moufang identities
The proof follows directly from fact (1).